Reply to Comment on 'Inverse problem from the discrete spectrum in the D = 2 dimensional space'

We want to thank our colleague F. Fernandez for his interest and his careful reading of our paper "The inverse problem from discrete spectrum in the D = 2 dimensional space". We are confused to have left a number of mistakes in the manuscript.

Discrete Sturm-Liouville equations with point interaction

Scattering solutions and several properties of scattering function of a discrete Sturm-Liouville boundary value problem with point interaction (PBVP) are derived. Moreover, resolvent operator, continuous and discrete spectrum of this PBVP are investigated. An asymptotic equation is utilized to get the properties of eigenvalues. An example illustrating the main results is given.

Dendrites and measures with discrete spectrum

We are interested in dendrites for which all invariant measures of zero-entropy mappings have discrete spectrum, and we prove that this holds when the closure of the endpoint set of the dendrites is countable. This solves an open question which has been around for awhile, and almost completes the characterization of dendrites with this property.

Coherent states for a system of an electron moving in a plane: case of discrete spectrum

In this work, we construct different classes of coherent states related to a quantum system, recently studied in [1], of an electron moving in a plane in uniform external magnetic and electric fields which possesses both discrete and continuous spectra. The eigenfunctions are realized as an orthonormal basis of a suitable Hilbert space appropriate for building the related coherent states. These latter are achieved in the context where we consider both spectra purely discrete obeying the criteria that a family of coherent states must satisfies.

Locating Ruelle–Pollicott resonances*

We study the spectrum of transfer operators associated to various dynamical systems. Our aim is to obtain precise information on the discrete spectrum. To this end we propose a unitary approach. We consider various settings where new information can be obtained following different branches along the proposed path. These settings include affine expanding Markov maps, uniformly expanding Markov maps, non-uniformly expanding or simply monotone maps, hyperbolic diffeomorphisms. We believe this approach could be greatly generalised.

Properties of 4ΛH Hypernucleus in Three-Cluster Microscopic Models

Within the framework of microscopic three-cluster algebraic models with possible consideration of clustering types (D + n) + Λ, (D + Λ) + n, and (n + Λ) + D, the properties of discrete spectrum states of hypernucleus 4ΛH and continuous spectrum states in the 3H + Λ channel are studied. It is shown that the cluster structure is almost completely determined by the clustering (D + n) + Λ with a rather appreciable effect from the polarization of the binary subsystem (D + n) due to its interaction with the Λ particle.